Right...each unit requires one resource, if it requires any at all. You can see how many of each resource you have left on the top of your screen. If you have zero horses, you can't build any horse-based units. If you build horses and then lose your supply (i.e. dip into negative horse resources), all of your horse units you have built already will suffer a huge combat penalty (-50% I believe).
Which units require resources should be listed in the civilopedia, or when you select the units from the build order it should show it there also. I'm not going to list them all but it's pretty straightforward...horse units ride horses, iron units wield swords, etc.